package com.ibm.cps.dft;

/*************************************************************************  
 *  Compilation:  javac Complex.java  
 *  Execution:    java Complex  
 *  
 *  Data type for complex numbers.  
 *  
 *  The data type is "immutable" so once you create and initialize  
 *  a Complex object, you cannot change it. The "final" keyword  
 *  when declaring re and im enforces this rule, making it a  
 *  compile-time error to change the .re or .im fields after  
 *  they've been initialized.  
 *  
 *  % java Complex  
 *  a            = 5.0 + 6.0i  
 *  b            = -3.0 + 4.0i  
 *  Re(a)        = 5.0  
 *  Im(a)        = 6.0  
 *  b + a        = 2.0 + 10.0i  
 *  a - b        = 8.0 + 2.0i  
 *  a * b        = -39.0 + 2.0i  
 *  b * a        = -39.0 + 2.0i  
 *  a / b        = 0.36 - 1.52i  
 *  (a / b) * b  = 5.0 + 6.0i  
 *  conj(a)      = 5.0 - 6.0i  
 *  |a|          = 7.810249675906654  
 *  tan(a)       = -6.685231390246571E-6 + 1.0000103108981198i  
 *  
 *************************************************************************/  
  
public class Complex   
{  
    private  double re;   // the real part  
    private  double im;   // the imaginary part  
  
    // create a new object with the given real and imaginary parts  
    public Complex(double real, double imag)   
    {  
        re = real;  
        im = imag;  
    }  
    
    /**
     * 
     * @param radis
     * @param xita
     * @param type: just used for differ from Complex#Complex(double real, double imag)
     */
    public Complex(double radis, double xita, int type)
    {
    	re = Math.cos(xita)*radis;
    	im = Math.sin(xita)*radis;
    }
  
    // return a string representation of the invoking Complex object  
    public String toString() {  
        if (im == 0) return re + "";  
        if (re == 0) return im + "i";  
        if (im <  0) return re + " - " + (-im) + "i";  
        return re + " + " + im + "i";  
    }  
  
    // return abs/modulus/magnitude and angle/phase/argument  
    public double abs()   { return Math.hypot(re, im); }  // Math.sqrt(re*re + im*im)  
    public double phase() { return Math.atan2(im, re); }  // between -pi and pi  
  
    // return a new Complex object whose value is (this + b)  
    public Complex plus(Complex b) {  
        Complex a = this;             // invoking object  
        double real = a.re + b.re;  
        double imag = a.im + b.im;  
        return new Complex(real, imag);  
    }  
    
    public void plusBy(Complex b) {  
        re = re + b.re;  
        im = im + b.im;  
    }
  
    /**  
     * return a new Complex object whose value is (this - b)  
     * @param b  
     * @return  
     */  
    public Complex minus(Complex b) {  
        Complex a = this;  
        double real = a.re - b.re;  
        double imag = a.im - b.im;  
        return new Complex(real, imag);  
    }
    
    public void minusBy(Complex b) {  
    	re = re - b.re;  
        im = im - b.im;  
    }
  
    /**  
     *  return a new Complex object whose value is (this * b)  
     * @param b 
     * @return  
     */  
    public Complex times(Complex b) {  
        Complex a = this;  
        double real = a.re * b.re - a.im * b.im;  
        double imag = a.re * b.im + a.im * b.re;  
        return new Complex(real, imag);  
    }
    
    public void timesBy(Complex b) {  
    	re = re * b.re - im * b.im;  
    	im = re * b.im + im * b.re;  
    }
  
    /**  
     *scalar multiplication  
     * return a new object whose value is (this * alpha)</br>  
     */  
    public Complex times(double alpha) {  
        return new Complex(alpha * re, alpha * im);  
    }  
    
    public void timesBy(double alpha) {  
    	re = alpha * re;  
    	im = im * alpha;  
    }  

  
    /**  
     *  return a new Complex object whose value is the conjugate of this
     */  
    public Complex conjugate() {  return new Complex(re, -im); }  
  
    /**  
     *  return a new Complex object whose value is the reciprocal of this
     */     
    public Complex reciprocal()  
    {  
        double scale = re*re + im*im;  
        return new Complex(re / scale, -im / scale);  
    }  
  
    /**  
     *  return the real part  
     * @return  
     */  
    public double re() { return re; }  
    /**  
     *  imaginary part  
     * @return  
     */  
    public double im() { return im; }  
  
    /**  
     *  return a / b  
     */  
    public Complex divides(Complex b)   
    {  
        Complex a = this;  
        return a.times(b.reciprocal());  
    }  
  
    // return a new Complex object whose value is the complex exponential of this  
    public Complex exp()   
    {  
        return new Complex(Math.exp(re) * Math.cos(im), Math.exp(re) * Math.sin(im));  
    }  
  
    // return a new Complex object whose value is the complex sine of this  
    public Complex sin()   
    {  
        return new Complex(Math.sin(re) * Math.cosh(im), Math.cos(re) * Math.sinh(im));  
    }  
  
    // return a new Complex object whose value is the complex cosine of this  
    public Complex cos()   
    {  
        return new Complex(Math.cos(re) * Math.cosh(im), -Math.sin(re) * Math.sinh(im));  
    }  
  
    // return a new Complex object whose value is the complex tangent of this  
    public Complex tan()   
    {  
        return sin().divides(cos());  
    }
    
    public double modulus()
    {
    	return Math.sqrt(re*re+im*im);
    }
      
    // a static version of plus  
    public static Complex plus(Complex a, Complex b)   
    {  
        double real = a.re + b.re;  
        double imag = a.im + b.im;  
        Complex sum = new Complex(real, imag);  
        return sum;  
    }  
  
    // sample client for testing  
    public static void main(String[] args) {  
        Complex a = new Complex(5.0, 6.0);  
        Complex b = new Complex(-3.0, 4.0);  
  
        System.out.println("a            = " + a);  
        System.out.println("b            = " + b);  
        System.out.println("Re(a)        = " + a.re());  
        System.out.println("Im(a)        = " + a.im());  
        System.out.println("b + a        = " + b.plus(a));  
        System.out.println("a - b        = " + a.minus(b));  
        System.out.println("a * b        = " + a.times(b));  
        System.out.println("b * a        = " + b.times(a));  
        System.out.println("a / b        = " + a.divides(b));  
        System.out.println("(a / b) * b  = " + a.divides(b).times(b));  
        System.out.println("conj(a)      = " + a.conjugate());  
        System.out.println("|a|          = " + a.abs());  
        System.out.println("tan(a)       = " + a.tan());  
    }  
  
}  